Hi,
The number is not unique for each pirated copy of the film, because the original film-makers don't need it to be unique.
What they will do, is produce a "batch" of films, each with a number - in the "LOTR: TROTK - Extended Edition (Region 3)" version, 820.
Batch 820 might go to a specific online site, or shop, or area. If a pirated version is then discovered, with that same batch number on it, the company producing the discs, and making the film itself, can track the pirate copy down to a specific location, shop or area. This is normally enough for the police or other law-enforcement agencies, to catch the individuals involved in producing the pirated release.
If every single DVD had a UIN (or Unique Identification Number), every single disc would need to be sold to people, in exchange for their personal details. This, would be cumbersome, and probably break many EU rules on Privacy, et al.
Obviously, it won't stop Joe or Jane Bloggs walking into a local store, buying a new film, and copying it, but it will stop (or at least slow down) people who make pirated copies of films from cinemas, preview discs, test discs, promotional release discs, and other similar places.
If a pirated disc is traced back to a shop, say for example Jane Bloggs' SuperStore, in High Street, London, the police or anti-piracy could go to the store, and request details of who and when each copy was sold. This could be traced via credit card details, security cameras, and other such information. This information can then be used to slowly reduce the list of potential pirates, from genuine customers, to the person/people actually committing the crime.
At least, that's what I've been led to believe is how the anti-piracy code numbers system works.
Pooch